Can the compositor be used to batch process images?
Yes, one not so elegant (no scripting :) but easy way to go about this would be to just use the Movie Clip node and point it to the directory with the images, pass it as input to your node group/compositor setup and render it out as an animation of stills or output each separately using the File Output node.

The only con or drawback to this approach is that the images need to be in a sequence for Blender to iterate through them.. img_001, img_002 ... img_00n or so you can scrub through in the clip editor or timeline but otherwise it should work as desired.